Ratios and percentages

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ellexay: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Jan 24, 2009 7:45 am; Thanked: 1 times

Ratios and percentages

by ellexay » Tue Feb 10, 2009 5:12 pm

There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.

A.1/4 B.1/5 C 1/6 D 1/7 E 1/8

Soln: What is the ratio of total wage of part time members to total wage of all members.

You have calculated ratio of Part time-to-Full time.

P x/4 3y/5 3xy/4*5
A 3x/4 Y + x/4 3y/5 18xy/20

Ratio= p/a= 3xy/18xy= 1/6

I don't really understand this solution the way it's presented. Please help!
Thank you all.

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Source: Beat The GMAT — Problem Solving | Tue Feb 10, 2009 5:12 pm

DeepakR: Master | Next Rank: 500 Posts; Posts: 158; Joined: Tue Sep 30, 2008 8:47 am; Thanked: 23 times; Followed by:1 members; GMAT Score:660

by DeepakR » Tue Feb 10, 2009 5:58 pm

Part time members = (25/100) (T) and
Full time members = (75/100) (T) where T= Total members

Let W= wage per hour and now the work time of part time members is given as, WP=3/5(WF).

Lets assume WF=15 i.e the full time members worked for 15hrs in a day hence WP=9.

So wage earned by 1 part time member = 9 * W= 9W and
wage earned by 1 Full time member = 15W

where W= wages per hour which is equal for both (as per question)

hence,
Total wage earned by all part time members = 9W * (25/100) * T --1
and
Total wage earned by all full time members = 15W * (75/100) *T --2

Total wage earned by all members = 54WT/4 --3

Dividing eq1 / eq3 we get,

[9W * T/4] / [54WT/4] = 1/6 = Ans.) C

- Deepak

Last edited by DeepakR on Tue Feb 10, 2009 6:22 pm, edited 1 time in total.

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pm; Location: Pittsburgh, PA; Thanked: 113 times; Followed by:27 members; GMAT Score:710

by dmateer25 » Tue Feb 10, 2009 6:12 pm

Let’s assume there are 4 workers
Part time = 1 worker
Full Time = 3 workers

Let’s assume the work time for a full time worker is 5 hours and therefore it would be 3 hours for a part time worker.

The wage = w
The part time to full time wage would be
3w/5*3w
3/15

Therefore the part time to the total wage would be
3/18 = 1/6

C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Dec 12, 2017 10:27 am

ellexay wrote:There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.

A.1/4 B.1/5 C 1/6 D 1/7 E 1/8

We can let the total staff members = x. Thus, 0.25x = part-time and 0.75x = full-time.

We can let f = the work time of each full-time member; thus, the work time of each part-time member is (3/5)f = 0.6f.

The total wage of the part-time members is (0.25x)(0.6f) = 0.15xf

The total wage for full-time members is 0.75xf.

Thus, the total wage for all members is 0.75xf + 0.15xf = 0.9xf, and the ratio of total wage of part-time members to total wage of all members is:

0.15xf/0.9xf = 15/90 = 1/6

Answer: C

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